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How to form a rectangle from the union of two Rectangles.

I'm trying to make a method called intersect that makes a Rectangle, my Rectangle class, which has a lower left corner point, a width, and a height, Rectangle(double x, double y, double width, double height);

I'm trying to figure out how to make a Rectangle that is is in common when the two intersect. i.e. where the Rectangle goes into another Rectangle, the Rectangle that forms. How do you get it's lower left point?

Also, how do you set it up to sorta copy the code for the Java Rectangle class for the method union, where I would get the union, or the smallest Rectangle that'll hold both Rectangles?